AFAIK, their war lay primarily in the Pacific, and beyond supporting the Brits and Russians materially, I’m not really sure why the US would want to involve themselves physically in the European theatre. I do feel fear of Germans beating them to the bomb might have something to do with it, but that’s just conjecture.
The campaign in Sicily and Italy started 5 months after the conclusion of the battle of Stalingrad.
What would Europe have looked like at the end of the war if American troops hadn't poured in?
Weren’t the Germans completely routed on the Eastern front post-Stalingrad?
Yes, and especially post-Kursk.
Why do you send in an army to win a war that your ally is already winning?